We analyze a nondegenerate three-level cascade laser coupled to a two-mode vacuum reservoir employing the stochastic differential equations associated with the normal ordering. We study the squeezing properties and entanglement amplification of the cavity radiation. We also calculate the correlation of the photon numbers and the fluctuations of the intensity difference. It turns out that the generated light exhibits a two-mode squeezing and entanglement when initially there are more atoms in the lower level. Moreover, a strong correlation between photon numbers along with a significant fluctuation in the intensity difference is found.

Analysis of the effects of external pumping on the quantum features of cavity radiation of the two-photon correlated emission laser is presented. It turns out that the pumping process induces the atomic coherence responsible for the entanglement of the cavity radiation as well as the correlation between the photon numbers belonging to different modes, despite the arising vacuum fluctuations. The photon number correlation is found to be very close to 2 where the entanglement is relatively better. Moreover, the mean number of photon pairs decreases with the amplitude of the driving radiation which is one of the practical limitations associated with the pumping mechanism. It is also shown that the mean photon number of the radiation in mode b is less than one-third of that in mode a.

We present the analysis of the effects of decoherence on quantum features of the cavity radiation of the two-photon-correlated emission laser, employing the stochastic differential equations associated with the normal ordering. We study how a thermal noise entering the cavity affects the squeezing, entanglement amplification, mean number of photon pairs and intensity difference in the cavity radiation. It turns out that the generated light exhibits a two-mode squeezing and entanglement when initially there are more atoms at the lower level, even when the cavity is coupled to a thermal reservoir. It is also found that though the thermal noise entering the cavity degrades the squeezing and entanglement, it significantly increases the mean number of photon pairs of the superimposed radiation.

Analysis of the effects of the biased noise fluctuations on the quantum features and statistical properties of the cavity radiation of the two-photon phase-sensitive laser is presented. It turns out that the biased noise fluctuations that enter the cavity via the vibrations of the wall enhance the atomic coherence responsible for the entanglement of the cavity radiation due to the phase sensitivity of the involved cascade transitions. The two-mode squeezing of the superimposed radiation, entanglement of the cavity radiation, and mean number of the photon pairs are found to increase with the rate at which the atoms are injected into the cavity. The two-mode squeezing increases with the intensity of the biased noise fluctuations, but the mean number of the photon pairs decreases. Even then, it is possible to produce quite intense robust continuous variable entanglement in this scheme which is believed to be a motivation for further practical scrutiny. Moreover, the superimposed radiation exhibits super-Poissonian photon statistics with no finite joint probability for getting more photons in mode b than mode a.

A detailed comparison among the exhibited nature of entanglement of the cavity radiation of the nondegenerate three-level cascade laser when different inseparability criteria are employed is presented. Although the achievable degree of entanglement is generally found to vary with the applied inseparability criteria, there are cases for which more than two of the applied criteria lead to a significant degree of entanglement for certain parameters. Particularly, the procedures following from the criterion of Duan–Geidke–Cirac–Zoller and logarithmic negativity predict a similar pattern of entanglement except when the atoms are initially prepared in a maximum atomic coherent superposition. In the same manner, in relation to the absence of interatomic interaction, the Hillery–Zubairy and Cauchy–Schwarz inequalities virtually lead to a similar degree of entanglement. Since an appreciably large degree of entanglement is shown to be realizable using various criteria, there is no doubt that this quantum system can be utilized as a viable source of entangled light.